Abstract
In Section 5 of the previous chapter a simple recursive algorithm was given for an appropriate transformation of the disturbances and the data of a regression model when the disturbances follow an MA(1) process. In the Sections 2 and 3 of this chapter auxiliary recursive formulae are derived in order to transform the disturbances ut as well as the data when the disturbances follow an arbitrary MA or ARMA process, and where the number of multiplications involved only increases linearly with the number of observations. Furthermore, it will be shown in this chapter in Section 4 how the method of Ansley (1979) in the case of ARMA(p,q) disturbances can be put in the framework of the previous chapter and how this leads to an algorithm for calculating |Γu| as well as v=L−1z where L is the lower triangular matrix such that LL’=Γz, i.e., the Cholesky decomposition; z is defined in Section 7 of the previous chapter.
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© 1991 Springer-Verlag Berlin Heidelberg
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Knottnerus, P. (1991). Computational Aspects of Data Transformations and Ansley’s Algorithm. In: Linear Models with Correlated Disturbances. Lecture Notes in Economics and Mathematical Systems, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48383-7_3
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DOI: https://doi.org/10.1007/978-3-642-48383-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53901-8
Online ISBN: 978-3-642-48383-7
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